Apr 25, 2015 · Parametrization is... the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.

Feb 6, 2025 · Is there a rigorous definition of parametrization? From what I can see, there is no absolute definition of parametrization, but simply a set of ideals that try to come to as close as possible: A

Feb 15, 2011 · The point is that parametrization helped you solve a system of equations that would normally be very difficult or impossible to solve explicitly.

Oct 17, 2014 · A parametrization of a straight line from P to Q is r(t) = tP + (1 − t)Q as t goes from 0 to 1. Four of these pieces with suitable start and stop values for t will take you round the square for t going …

Jul 20, 2015 · and this second parametrization is regular because its velocity anywhere is at least 1. So, my question is: given a non-regular parametrization of a curve, is there an algorithm to tell whether …

Jul 15, 2018 · Other answers are correct, shortest explanation: set x=0 in your equation to see the y intercept is sqrt (2), not 1.

Dec 30, 2021 · The parametrization doesn't need to be injective as long as it only ever maps finitely many points together. My best attempt to construct a parametrization would be to construct smooth …

Arc length parametrization just means unit speed parametrization. The former is used for some dumb historical reasons, I think the latter is far clearer.

Apr 13, 2005 · This parametrization would give us a different set of points on the paraboloid, but they would still lie on the same surface. It is important to note that there are many possible ways to …

Jun 5, 2021 · 5 I need to find the rational parametrization of the complex curve with affine equation y2 − 6x2y − 3x4 + 4x3y + 4x3 = 0. y 2 6 x 2 y 3 x 4 + 4 x 3 y + 4 x 3 = 0. I did find a solution, I don't know …